"developers need to think about the stability of the product as just as important as the features"
It's about doing your job properly then?
You may have guessed that I'm rather cynical about this sort of stuff. Along with Agile and eXtreme (bloody stupid name). Whenever I hear any of these names I think of spotty youths who can't be bothered to actually design something right the first time round and cirtainly can't be arsed to document anything.
And even if I get over my cynicism for a moment, it all assumes that the system you're working on can tolerate a half baked broken change. I've never worked on anything that can be anything other than working perfectly. You might get away with it on faecesbook or some such but contrary to what many seem to believe, not all software is related to running a web site. And your fancy DevOps etc often doesn't work in other environments